Mathematics Commons^™

Extension Of Refinement Rings, Rahman Bahmani Sangesari, Marjan Sheibani Abdulyousefi, Nahid Ashrafi

Turkish Journal of Mathematics

In this paper we prove that a ring $R$ in which every finitely generated projective $R$-module lifts modulo $J(R)$ is a refinement ring if and only if $ \frac{R}{J(R)}$ is a refinement ring. We also prove that the refinement property for rings is Morita invariant. Several examples are constructed as well.

Homothetic Motions With Dual Octonions In Dual $8-$Space, Hesna Kabadayi

Turkish Journal of Mathematics

In this study, for dual octonions in dual $8-$space $D^{8}$ over the domain of coefficients $D,$ we give a matrix that is similar to a Hamilton operator. By means of this matrix a new motion is defined and this motion is proven to be homothetic. For this one parameter dual homothetic motion, we prove some theorems about dual velocities, dual pole points, and dual pole curves. Furthermore, after defining dual accelerations, we show that the motion defined by the regular order $m$ dual curve, at every $t$-instant, has only one acceleration center of order $\left( m-1\right) .$

Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang

Turkish Journal of Mathematics

Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule, and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules over $T$, and discuss when a left $T$-module is a strongly Gorenstein projective or strongly Gorenstein injective module.

An Extension Of Cline''S Formula For A Generalized Drazin Inverse, Haifeng Lian, Qingping Zeng

Turkish Journal of Mathematics

In this note we give an answer to a question recently posed by Zeng and Zhong, to note that Cline's formula for a generalized Drazin inverse extends to the case when $aba=aca$. Cline's formula for a pseudo Drazin inverse is also presented in this case.

On The Twisted Modules For Finite Matrix Groups, Kübra Gül, Nurullah Ankaralioğlu

Turkish Journal of Mathematics

Suppose that $W$ is an irreducible $F_{q}G$-module of dimension $n$ $% (d^{2}

A Presentation And Some Finiteness Conditions For A New Version Of The Schützenberger Product Of Monoids, Eylem Güzel Karpuz, Firat Ateş, Ahmet Si̇nan Çevi̇k, İsmai̇l Naci̇ Cangül

Turkish Journal of Mathematics

In this paper we first define a \textit{new version} of the Sch\"{u}tzenberger product for any two monoids $A$ and $B$, and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.

On The Finite $P$-Groups With Unique Cyclic Subgroup Of Given Order, Libo Zhao, Yangming Li, Lu Gong

Turkish Journal of Mathematics

In this paper, we prove that if $G$ is nonabelian and $ G >p^4$, then $G$ has a unique cyclic subgroup of order $p^m$ with $m\geq 3$ if and only if $G$ has a unique abelian subgroup of order $p^3$ if and only if $G$ is a $2$-group of maximal class.

Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind, Maryam Shams Solary

Turkish Journal of Mathematics

We derive a generalization for the reconstruction of $M$-sparse sums in Chebyshev bases of the third and fourth kind. This work is used for a polynomial with Chebyshev sparsity and samples on a Chebyshev grid of $[-1,1]$. Further, fundamental reconstruction algorithms can be a way for getting M-sparse expansions of Chebyshev polynomials of the third and fourth kind. The numerical results for these algorithms are designed to compare the time effects of doing them.

The Dual Generalized Chernoff Inequality For Star-Shaped Curves, Deyan Zhang, Yunlong Yang

Turkish Journal of Mathematics

In this paper, we first introduce the $k$-order radial function $\rho_k(\theta)$ for star-shaped curves in $\mathbb{R}^2$ and then prove a geometric inequality involving $\rho_k(\theta)$ and the area $A$ enclosed by a star-shaped curve, which can be looked upon as the dual Chernoff--Ou--Pan inequality. As a by-product, we get a new proof of the classical dual isoperimetric inequality. We also prove that $\frac{C^2}{k^2}\leq A

Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic, Firdous Ahmad Shah, Mohammad Younus Bhat

Turkish Journal of Mathematics

Orthogonal wavelet packets lack symmetry, which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of Fourier transforms. We also show how to obtain several new Riesz bases of the space $L^2(K)$ by constructing a series of subspaces of these wavelet packets. Finally, we provide algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.

Weakly $2$-Absorbing Submodules Of Modules, Sedigheh Moradi, Abdulrasool Azizi

Turkish Journal of Mathematics

Let $M$ be a module over a commutative ring $R.$ A proper submodule $N$ of $M$ is called weakly $2$-absorbing, if for $r,s\in R$ and $x\in M$ with $0\neq rsx\in N,$ either $rs\in (N:M)$ or $rx\in N$ or $sx\in N.$ We study the behavior of $(N:M)$ and $\sqrt{(N:M)},$ when $N$ is weakly $2$-absorbing. The weakly $2$-absorbing submodules when $R=R_1\oplus R_2$ are characterized. Moreover we characterize the faithful modules whose proper submodules are all weakly $2$-absorbing.

Some Results And Examples On Difference Cordial Graphs, Mohammed Seoud, Shakir Salman

Turkish Journal of Mathematics

In this paper we introduce some results on difference cordial graphs and describe the difference cordial labeling for some families of graphs.

A Measure Theoretic Approach To Problems Of Number Theory With Applications To The Proof Of The Prime Number Theorem, Russell Lee Jahn

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper we demonstrate how the principles of measure theory can be applied effectively to problems of number theory. Initially, necessary concepts from number theory will be presented. Next, we state standard concepts and results from measure theory to which we will need to refer. We then develop our repertoire of measure theoretic machinery by constructing the needed measures and defining a generalized version of the multiplicative convolution of measures. A suitable integration by parts formula, one that is general enough to handle various combinations of measures, will then be derived. At this juncture we will be ready to …

Multi-Type Display Calculus For Propositional Dynamic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

We introduce a multi-type display calculus for Propositional Dynamic Logic (PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style cut-elimination and subformula property.

Teachers' Perceptions Of Manipulatives During Middle School Math Instruction, Angela L. Vizzi

Walden Dissertations and Doctoral Studies

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district's math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers' perceptions of PD and perceived …

Tool Support For Reasoning In Display Calculi, Samuel Balco, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, …

Existence And Classification Of Nonoscillatory Solutions Of Two Dimensional Time Scale Systems, Özkan Özturk

Doctoral Dissertations

"During the past years, there has been an increasing interest in studying oscillation and nonoscillation criteria for dynamic equations and systems on time scales that harmonize the oscillation and nonoscillation theory for the continuous and discrete cases in order to combine them in one comprehensive theory and eliminate obscurity from both.

We not only classify nonoscillatory solutions of dynamic equations and systems on time scales but also guarantee the (non)existence of such solutions by using the Knaster fixed point theorem, Schauder - Tychonoff fixed point theorem, and Schauder fixed point theorem. The approach is based on the sign of nonoscillatory …

Boundary Control Of Parabolic Pde Using Adaptive Dynamic Programming, Behzad Talaei

Doctoral Dissertations

"In this dissertation, novel adaptive/approximate dynamic programming (ADP) based state and output feedback control methods are presented for distributed parameter systems (DPS) which are expressed as uncertain parabolic partial differential equations (PDEs) in one and two dimensional domains. In the first step, the output feedback control design using an early lumping method is introduced after model reduction. Subsequently controllers were developed in four stages; Unlike current approaches in the literature, state and output feedback approaches were designed without utilizing model reduction for uncertain linear, coupled nonlinear and two-dimensional parabolic PDEs, respectively. In all of these techniques, the infinite horizon cost …

Pointwise And Uniform Convergence Of Fourier Series On Su(2), Donald Forrest Myers

Doctoral Dissertations

"Let f be a Lipschitz function on the special unitary group SU (2). We prove that the Fourier partial sums of f converge to f uniformly on SU (2), thereby extending theorems of Caccioppoli, Mayer, and a special case of Ragozin. Pointwise convergence theorems for the Fourier series of functions on SU (2), due to Liu and Qian, were obtained by Clifford algebra techniques. We obtain similar versions of these theorems using simpler proof techniques: classical harmonic analysis and group theory"--Abstract, page iii.

Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c+t) in the direction …